Abstract
The importance and usefulness of fractal dimension in describing surface roughness over the conventional roughness parameters are presented in this chapter. The fundamental of fractal dimension and the methodology for evaluation of fractal dimension are also discussed. Literature survey is carried out for four different types of machining processes and shows that there is scarcity of literatures which deal with fractal description of surface roughness. Fundamentals of design of experiments and response surface methodology are also discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abburi NR, Dixit US (2006) A knowledge-based system for the prediction of surface roughness in turning process. Robotics Comput-Integr Manuf 22:363–372
Abouelatta OB, Madl J (2001) Surface roughness prediction based on cutting parameters and tool vibrations in turning operations. J Mater Process Technol 118:269–277
Alauddin M, El Baradie MA, Hashmi MSJ (1996) Optimization of surface finish in end milling Inconel 718. J Mater Process Technol 56:54–65
Amorima FL, Weingaertner WL (2005) The influence of generator actuation mode and process parameters on the performance of finish EDM of a tool steel. J Mater Process Technol 166:411–416
Arbizu IP, Pérez CJL (2003) Surface roughness prediction by factorial design of experiments in turning processes. J Mater Process Technol 143–144:390–396
Assarzadeh S, Ghoreishi M (2008) Neural-network-based modeling and optimization of the electro-discharge machining process. Int J Adv Manuf Technol 39:488–500
Bagci E, Aykut S (2006) A study of Taguchi optimization method for identifying optimum surface roughness in CNC face milling of cobalt-based alloy (stellite 6). Int J Adv Manuf Technol 29:940–947
Bagci E, Isik B (2006) Investigation of surface roughness in turning unidirectional GFRP composites by using RS methodology and ANN. Int J Adv Manuf Technol 31:10–17
Balic J, Korosec M (2002) Intelligent tool path generation for milling of free surfaces using neural networks. Int J Mach Tools Manuf 42:1171–1179
Benardos PG, Vosniakos GC (2002) Prediction of surface roughness in CNC face milling using neural networks and Taguchi’s design of experiments. Robotics Comput-Integr Manuf 18:343–354
Benardos PG, Vosniakos GC (2003) Predicting surface roughness in machining: a review. Int J Mach Tools Manuf 43(8):833–844
Berglund J, Rose’n BG (2009) A method development for correlation of surface finish appearance of die surfaces and roughness measurement data. Tribol Lett 36(2):157–164
Berry MV, Lewis ZV (1980) On the Weierstrass-Mandelbrot fractal function. Proc R Soc A 370:459–484
Bhushan B, Wyant JC, Meiling J (1988) A new three-dimensional non-contact digital optical profiler. Wear 122:301–312
Bigerelle M, Najjar D, Iost A (2005) Multiscale functional analysis of wear a fractal model of the grinding process. Wear 258:232–239
Brown CA, Savary G (1991) Describing ground surface texture using contact profilometry and fractal analysis. Wear 141:211–226
Chang CK, Lu HS (2007) Design optimization of cutting parameters for side milling operations with multiple performance characteristics. Int J Adv Manuf Technol 32:18–26
Chavoshi SZ, Tajdari M (2010) Surface roughness modelling in hard turning operation of AISI 4140 using CBN cutting tool. Int J Mater Form. doi:10.1007/s12289-009-0679-2
Choi TJ, Subrahmanya N, Li H, Shin YC (2008) Generalized practical models of cylindrical plunge grinding processes. Int J Mach Tools Manuf 48:61–72
Dabnun MA, Hashmi MSJ, El-Baradie MA (2005) Surface roughness prediction model by design of experiments for turning machinable glass-ceramic (Macor). J Mater Process Technol 164–165:1289–1293
Davim JP (2001) A note on the determination of optimal cutting conditions for surface finish obtained in turning using design of experiments. J Mater Process Technol 116:305–308
El-Sonbaty IA, Khashaba UA, Selmy AI, Ali AI (2008) Prediction of surface roughness profiles for milledsurfaces using an artificial neural network and fractal geometry approach. J Mater Process Technol 200:271–278
Feng CX, Wang XF (2003) Surface roughness predictive modeling: neural networks versus regression. IIE Trans 35:11–27
Feng CXJ, Yu ZG, Kusiak A (2006) Selection and validation of predictive regression and neural network models based on designed experiments. IIE Trans 38:13–23
Fredj NB, Amamou R (2006) Ground surface roughness prediction based upon experimental design and neural network models. Int J Adv Manuf Technol 31:24–36
Fuh KH, Wu CF (1995) A proposed statistical model for surface quality prediction in end-milling of Al alloy. Int J Mach Tools Manuf 35(S):1187–1200
Ge S, Chen G (1999) Fractal prediction models of sliding wear during the running–in process. Wear 231:249–255
Ghani JA, Choudhury IA, Hassan HH (2004) Application of Taguchi method in the optimization of end milling parameters. J Mater Process Technol 145:84–92
Grzesik W (1996) A revised model for predicting surface roughness in turning. Wear 194:143–148
Gupta AK (2010) Predictive modelling of turning operations using response surface methodology, artificial neural networks and support vector regression. Int J Prod Res 48(3):763–778
Han JH, Ping S, Shengsun H (2005) Fractal characterization and simulation of surface profiles of copper electrodes and aluminum sheets. Mater Sci Eng A 403:174–181
Hasegawa M, Liu J, Okuda K, Nunobiki M (1996) Calculation of the fractal dimensions of machined surface profiles. Wear 192:40–45
Hassui A, Diniz AE (2003) Correlating surface roughness and vibration on plunge cylindrical grinding of steel. Int J Mach Tools Manuf 43:855–862
He L, Zhu J (1997) The fractal character of processed metal surfaces. Wear 208:17–24
Hecker RL, Liang SY (2003) Predictive model of surface roughness in grinding. Int J Mach Tools Manuf 43:755–761
ISO 4287:1997 (1997) Geometrical product specification (GPS)—surface texture: profile method—terms, definitions and surface texture parameters. International Organization of Standardization, Geneva
Jahn R, Truckenbrodt H (2004) A simple fractal analysis method of the surface roughness. J Mater Process Technol 145:40–45
Jesuthanam CP, Kumanan S, Asokan P (2007) Surface roughness prediction using hybrid neural networks. Mach Sci Technol 11:271–286
Jiang Z, Wang H, Fei B (2001) Research into the application of fractal geometry in characterizing machined surfaces. Int J Mach Tools Manuf 41:2179–2185
Jiao Y, Lei S, Pei ZJ, Lee ES (2004) Fuzzy adaptive networks in machining process modeling: surface roughness prediction for turning operations. Int J Mach Tools Manuf 44:1643–1651
Kang MC, Kim JS, Kim KH (2005) Fractal dimension analysis of machined surface depending on coated tool wear. Surf Coat Technol 193(1–3):259–265
Karayel D (2009) Prediction and control of surface roughness in CNC lathe using artificial neural network. J Mater Process Technol 209:3125–3137
Keskin YH, Halkacı HS, Kizil SM (2006) An experimental study for determination of the effects of machining parameters on surface roughness in electrical discharge machining (EDM). Int J Adv Manuf Technol 28:1118–1121
Kirby ED, Zhang Z, Chen JC, Chen J (2006) Optimizing surface finish in a turning operation using the Taguchi parameter design method. Int J Adv Manuf Technol 30:1021–1029
Kohli A, Dixit US (2005) A neural-network-based methodology for the prediction of surface roughness in turning process. Int J Adv Manuf Technol 25:118–129
Krajnik P, Kopac J, Sluga A (2005) Design of grinding factors based on response surface methodology. J Mater Process Technol 162–163:629–636
Kwak JS (2005) Application of Taguchi and response surface methodologies for geometric error in surface grinding process. Int J Mach Tools Manuf 45:327–334
Kwak JS, Sim SB, Jeong YD (2006) An analysis of grinding power and surface roughness in external cylindrical grinding of hardened SCM440 steel using response surface method. Int J Mach Tools Manuf 46:304–312
Lee SH, Li XP (2001) Study of the effect of machining parameters on the machining characteristics in electrical discharge machining of tungsten carbide. J Mater Process Technol 115:344–358
Lee KY, Kang MC, Jeong YH, Lee DW, Kim JS (2001) Simulation of surface roughness and profile in high-speed end milling. J Mater Process Technol 113:410–4125
Lin TR (2002) Optimisation technique for face milling stainless steel with multiple performance characteristics. Int J Adv Manuf Technol 19:330–335
Lin JL, Lin CL (2002) The use of orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics. Int J Mach Tools Manuf 42:237–244
Lin JL, Lin CL (2005) The use of grey-fuzzy logic for the optimization of the manufacturing process. J Mater Process Technol 160:9–14
Lin WS, Lee BY, Wu CL (2001) Modeling the surface roughness and cutting force for turning. J Mater Process Technol 108:286–293
Ling FF (1990) Fractals, engineering surfaces and tribology. Wear 136:141–156
Lou MS, Chen JC, Li CM (1998) Surface roughness prediction technique for CNC end-milling. J Ind Technol 15 (1), November 1998 to January 1999
Majumdar A, Bhushan B (1990) Role of fractal geometry in roughness characterization and contact mechanics of surfaces. Trans ASME J Tribol 112:205–216
Majumdar A, Tien CL (1990) Fractal characterization and simulation of rough surfaces. Wear 136:313–327
Maksoud TMA, Atia MR, Koura MM (2003) Applications of artificial intelligence to grinding operations via neural networks. Mach Sci Technol 7(3):361–387
Mandal D, Pal SK, Saha P (2007) Modeling of electrical discharge machining process using back propagation neural network and multi-objective optimization using non-dominating sorting algorithm-II. J Mater Process Technol 186:154–162
Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638
Mandelbrot BB (1982) The fractal geometry of nature. W H freeman, New York
Mansour A, Abdalla H (2002) Surface roughness model for end milling: a semi-free cutting carbon casehardening steel (EN32) in dry condition. J Mater Process Technol 124:183–191
Minitab User Manual Release 13.2 (2001) Making data analysis easier. MINITAB Inc. State College, PA
Mohanasundararaju N, Sivasubramanian R, Gnanaguru R, Alagumurthy N (2008) A neural network and fuzzy-based methodology for the prediction of work roll surface roughness in a grinding process. Int J Comput Methods Eng Sci Mech 9:103–110
Montgomery DC (2001) Design and analysis of experiments. Wiley, New York
Muthukrishnan N, Davim JP (2009) Optimization of machining parameters of Al/SiC-MMC with ANOVA and ANN analysis. J Mater Process Technol 209:225–232
Nalbant M, Gokkaya H, Sur G (2007) Application of Taguchi method in the optimization of cutting parameters for surface roughness in turning. Mater Des 28:1379–1385
Nayak PR (1971) Random process model of rough surfaces. Trans ASME J Lubr Technol 93:398–407
Öktem H (2009) An integrated study of surface roughness for modeling and optimization of cutting parameters during end milling operation. Int J Adv Manuf Technol 43:852–861
Oktem H, Erzurumlu T, Kurtaran H (2005) Application of response surface methodology in the optimization of cutting conditions for surface roughness. J Mater Process Technol 170:11–16
Pal SK, Chakraborty D (2005) Surface roughness prediction in turning using artificial neural network. Neural Comput Appl 14:319–324
Palanikumar K (2008) Application of Taguchi and response surface methodologies for surface roughness in machining glass fiber reinforced plastics by PCD tooling. Int J Adv Manuf Technol 36:19–27
Palanikumar K, Karunamoorthy L, Karthikeyan R (2006) Parametric optimization to minimise the surface roughness on the machining of GFRP composites. J Mater Sci Technol 22(1):66–72
Petropoulos G, Vaxevanidis NM, Pandazaras C (2004) Modeling of surface finish in electro-discharge machining based upon statistical multi-parameter analysis. J Mater Process Technol 155–156:1247–1251
Puertas I, Luis CJ (2003) A study on the machining parameters optimisation of electrical discharge machining. J Mater Process Technol 143–144:521–526
Puertas I, Luis CJ, Álvarez L (2004) Analysis of the influence of EDM parameters on surface quality, MRR and EW of WC-Co. J Mater Process Technol 153–154:1026–1032
Puertas I, Luis CJ, Villa G (2005) Spacing roughness parameters study on the EDM of silicon carbide. J Mater Process Technol 164–165:1590–1596
Ramakrishnan R, Karunamoorthy L (2006) Multi response optimization of wire EDM operations using robust design of experiments. Int J Adv Manuf Technol 29:105–112
Ramasawmy H, Blunt L (2002) 3D surface characterisation of elctropolished EDMed surface and quantitative assessment of process variables using Taguchi Methodology. Int J Mach Tools Manuf 42:1129–1133
Ramasawmy H, Blunt L (2004) Effect of EDM process parameters on 3D surface topography. J Mater Process Technol 148:155–164
Ramesh S, Karunamoorthy L, Palanikumar K (2008) Surface roughness analysis in machining of titanium alloy. Mater Manuf Process 23:174–181
Reddy NSK, Rao PV (2005) Selection of optimum tool geometry and cutting conditions using a surface roughness prediction model for end milling. Int J Adv Manuf Technol 26:1202–1210
Reddy NSK, Rao PV (2006a) Experimental investigation to study the effect of solid lubricants on cutting forces and surface quality in end milling. Int J Mach Tools Manuf 46:189–198
Reddy NSK, Rao PV (2006b) Selection of an optimal parametric combination for achieving a better surface finish in dry milling using genetic algorithms. Int J Adv Manuf Technol 28:463–473
Routara BC, Bandyopadhyay A, Sahoo P (2009) Roughness modeling and optimization in CNC end milling using response surface method: effect of workpiece material variation. Int J Adv Manuf Technol 40:1166–1180
Sahin Y, Motorcu AR (2005) Surface roughness model for machining mild steel with coated carbide tool. Mater Des 26:321–326
Sahoo P (2005) Engineering tribology. Prentice Hall of India, New Delhi
Sahoo P, Ghosh N (2007) Finite element contact analysis of fractal surfaces. J Phys D Appl Phys 40:4245–4252
Sahoo P, Routara BC, Bandyopadhyay A (2009) Roughness modeling and optimization in EDM using response surface method for different workpiece materials. Int J Mach Mach Mater 5(2–3):321–346
Sarkar S, Mitra S, Bhattacharyya B (2006) Parametric optimisation of wire electrical discharge machining of γ titanium aluminide alloy through an artificial neural network model. Int J Adv Manuf Technol 27:501–508
Sayles RS, Thomas TR (1978) Surface topography as a non-stationary random process. Nature 271:431–434
Shah A, Mufti NA, Rakwal D, Bamberg E (2010) Material removal rate, kerf, and surface roughness of tungsten carbide machined with wire electrical discharge machining. J Mater Eng Perform. doi:10.1007/s11665-010-9644-y
Siddiquee AN, Khan ZA, Mallick Z (2010) Grey relational analysis coupled with principal component analysis for optimisation design of the process parameters in in-feed centreless cylindrical grinding. Int J Adv Manuf Technol 46:983–992
Singh D, Rao PV (2007) A surface roughness prediction model for hard turning process. Int J Adv Manuf Technol 32:1115–1124
Spedding TA, Wang ZQ (1997) Parametric optimization and surface characterization of wire electrical discharge machining process. Precis Eng 20:5–15
Suresh PVS, Rao PV, Deshmukh SG (2002) A genetic algorithm approach for optimization of surface roughness prediction model. Int J Mach Tools Manuf 42:675–680
Thomas TR (1982) Defining the microtopography of surfaces in thermal contact. Wear 79:73–82
Tricot C, Ferlans P, Baran G (1994) Fractal analysis of worn surfaces. Wear 172:127–133
Tsai KM, Wang PJ (2001) Predictions on surface finish in electrical discharge machining based upon neural network models. Int J Mach Tools Manuf 41:1385–1403
Tsai YH, Chen JC, Lou SJ (1999) An in-process surface recognition system based on neural networks in end milling cutting operations. Int J Mach Tools Manuf 39:583–605
Venkatesh K, Bobji MS, Biswas SK (1998) Some features of surface topographical power spectra generated by conventional machining of a ductile metal. Mater Sci Eng A A252:153–155
Venkatesh K, Bobji MS, Gargi R, Biswas SK (1999) Genesis of workpiece roughness generated in surface grinding and polishing of metals. Wear 225–229:215–226
Wang MY, Chang HY (2004) Experimental study of surface roughness in slot end milling AL2014–T6. Int J Mach Tools Manuf 44:51–57
Whitehouse DJ (1982) The parameter rash, is there a cure? Wear 83:75–78
Yan W, Komvopoulos K (1998) Contact analysis of elastic-plastic fractal surfaces. J Appl Phys 84(7):3617–3624
Yang JL, Chen JC (2001) A systematic approach for identifying optimum surface roughness performance in end-milling operations. J Ind Technol 17, 2 February 2001 to April 2001
Yang WH, Tarng YS (1998) Design optimization of cutting parameters for turning operations based on the Taguchi method. J Mater Process Technol 84:122–129
Yih-fong T, Fu-chen C (2003) A simple approach for robust design of high-speed electrical discharge machining technology. Int J Mach Tools Manuf 43:217–227
Zain AM, Haron H, Sharif S (2010a) Application of GA to optimize cutting conditions for minimizing surface roughness in end milling machining process. Expert Syst Appl 37:4650–4659
Zain AM, Haron H, Sharif S (2010b) Prediction of surface roughness in the end milling machining using artificial neural network. Expert Syst Appl 37:1755–1768
Zhang JZ, Chen JC (2007) The development of an in-process surface roughness adaptive control system in end milling operations. Int J Adv Manuf Technol 31:877–887
Zhang JH, Lee TC, Lau WS (1997) Study on the electro-discharge machining of a hot pressed aluminum oxide based ceramic. J Mater Process Technol 63:908–912
Zhang Y, Luo Y, Wang JF, Li Z (2001) Research on the fractal of surface topography of grinding. Int J Mach Tools Manuf 41:2045–2049
Zhong ZW, Khoo LP, Han ST (2006) Prediction of surface roughness of turned surfaces using neural networks. Int J Adv Manuf Technol 28:688–693
Zhong ZW, Khoo LP, Han ST (2008) Neural-network predicting of surface finish or cutting parameters for carbide and diamond turning processes. Mater Manuf Process 23:92–97
Zhou X, Xi F (2002) Modeling and predicting surface roughness of the grinding process. Int J Mach Tools Manuf 42:969–977
Zhu H, Ge S, Huang X, Zhang D, Liu J (2003) Experimental study on the characterization of worn surface topography with characteristic roughness parameter. Wear 255:309–314
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Prasanta Sahoo
About this chapter
Cite this chapter
Sahoo, P., Barman, T., Davim, J.P. (2011). Fundamental Consideration. In: Fractal Analysis in Machining. SpringerBriefs in Applied Sciences and Technology(), vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17922-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-17922-8_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17921-1
Online ISBN: 978-3-642-17922-8
eBook Packages: EngineeringEngineering (R0)